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arXiv:quant-ph/0607114 · Physical Review A

Relationship between resolution enhancement and multiphoton absorption rate in quantum lithography

Mankei Tsang

Published Apr 20, 2007• 38 citations

Abstract

The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.'s heuristic claim, the multiphoton absorption rate of a $(\ensuremath{\mid}N,0⟩+\ensuremath{\mid}0,N⟩)$ quantum state is actually lower than that of a classical state with otherwise identical parameters. The proof-of-concept experiment of quantum lithography [D'Angelo et al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the proposed formalism, and the experiment is shown to have a reduced multiphoton absorption rate in order to emulate quantum lithography accurately. Finally, quantum lithography by the use of a jointly Gaussian quantum state of light is investigated to illustrate the trade-off between resolution enhancement and multiphoton absorption rate.

DOI: 10.1103/physreva.75.043813

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The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.'s heuristic claim, the multiphoton absorption rate of a

(\ensuremath{\mid}N,0⟩+\ensuremath{\mid}0,N⟩)

quantum state is actually lower than that of a classical state with otherwise identical parameters. The proof-of-concept experiment of quantum lithography [D'Angelo et al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the proposed formalism, and the experiment is shown to have a reduced multiphoton absorption rate in order to emulate quantum lithography accurately. Finally, quantum lithography by the use of a jointly Gaussian quantum state of light is investigated to illustrate the trade-off between resolution enhancement and multiphoton absorption rate.

The concept of performing quantum lithography with classical, instead of entangled, light is of great interest for practical implementation. One recent proposal [Hemmer, Muthukrishnan, Scully, and Zubairy, Phys. Rev. Lett. 96, 163603 (2006)] to accomplish this was based on the use of frequency selective multiphoton transitions in a two-level atom. To analyze this possibility we investigate a four-level system theoretically and show that a high-resolution lithography is possible. We quantitatively identify conditions under which high-contrast lithography can be performed without sacrificing high resolution. The approach is a perturbative density matrix method. This model identifies the tradeoff between resolution and contrast as being due to higher-order terms from intermediate-level Rabi oscillations. We propose using positive and negative one-photon detunings to suppress this effect. Allowing higher Rabi frequencies means that shorter interaction time can be used, and this overcomes the degradation in contrast due to population decay. Finally, we generalize our scheme to $\mathbit{N}$-photon lithography.

Summary form only given. Recently, Boto et al. (see Phys. Rev. Lett., vol. 85, p. 2773, 2000) showed that using N entangled photons and an N-photon responsive lithographic recording medium, one could potentially write lithographic gratings with a resolution that is N times better than the classical Rayleigh criterion. An anticipated experimental difficulty is that such beams are weak, yet strong fields are needed to excite the N-photon absorption process. For the case of N=2, which was described in detail by Boto et al., we propose a method to overcome this problem. We also propose to use this idea "in reverse" to perform microscopy with better resolution than aloowed by the Rayleigh limit.